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Sensitive absorption measurements can expose irregularly shaped vibrational overtone bands from the near-IR well into the visible region for stretching modes involving light atoms - particularly hydrogen. For the fifth overtone transition of the C-H stretching mode of liquid benzene, the asymmetric shape has been modelled as Franck-Condon structure in the separate rolibrational space of the molecule. The two rolibrational potentials, one for the ground state, the other for the fifth overtone state, were approximated as truncated anharmonic wells. In the present work the rolibrational potentials are treated as periodic cosinusoids and the associated Franck-Condon structure is derived in which one can smoothly pass from hindered rotation to free rotation, which is particularly relevant to potential barriers that are on the order of kT of less. Application to benzene provides a fit to the shape of the asymmetric fifth overtone band that is essentially within experimental error. The symbolic capabilities of Mathematica (ver. 3.0) have greatly facilitated the calculations by providing a quasi-analytic approach valid over a large range of parameters.
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